Set oven to 350°F.
Sprinkle half the creole seasoning on top and bottom of chicken breasts. Then lay chicken breasts skin down into an 8x by 8x baking dish. Cover with tin foil and bake for an hour.
Chop up your onion, celery, red and green bell peppers and your garlic.
In a large soup pot or dutch oven add your olive oil. Turn heat to hight and when it starts to get hot add your veggies. Sweat them for at least 3 minutes before adding the rest of the creole seasoning, the chicken stock, bay leaf, black pepper and thyme. Bring to a boil and then turn to Med-Low.
When the hour is up take the chicken out of the oven and let rest for 5-10 minutes. Once rested and cooled you'll want to take the chicken off the bone and add meat to the pot of simmering soup. Discard all skin and bones but add the juices at the bottom of your baking dish to your pot. Add green beans. Let simmer about 10 minutes.
In a mixing bowl combine flour, baking powder, parsley, pepper, salt, eggs and water until it looks like a thick paste. You may need to add another teaspoon or two of water depending on the size of your eggs.
Turn heat back up to Med-High until it's brought to a heavy boil. Using two teaspoons spoon the dumpling mixture teaspoon by teaspoon into the soup. Once all the dumplings have bounced back up to the surface you know they are done. Turn heat back down to low and let simmer for about 5 minutes before serving.